Just skimmed it, but in principle I agree completely, and this is how I tend to approach learning math-related things. I'm pretty bad at just memorizing long, complex formulas, but if I can figure out what the formula is DOING, then it clicks, and in a pinch I know I can derrive it backwards if I have to. For example, something I have to do relatively often is annualize returns. You link returns in the first place by multiplying the return relatives (the terminal value of one unit grown at the rate of return for the period - for 5%, that'd be 1.05) to generate a cumulative return relative for the entire series, and then convert back into return format by subtracting 1 and multiplying by 100 (i.e - 1.2301 becomes 23.01%). But, if that's a period longer than a year, you're often interested in what the average return *per year* is for the period in question, so you need to take the geometric average. At that point, it's a bit of logic. Because you link returns in a multiplicative manner, you need to raise them to a fractional power to calculate the average annual rate for a given number of periods. So, what's the conversion ratio? Logically, the number of periods per year divided by the total number of periods.

I think math makes much more sense once you can "see" what an equation is doing, and why. Not only does it make more sense to you when you do, but if you ever forget an equation you can usually work it out (I can never remember if it's total periods over periods per year or vice versa in the above example, but a moment to think about it and it becomes clear).

I think all subjects should be taught like this, if possible. Less of a focus on rote repetition and memorization, and more on how and why.